ZEN, a new toolbox
for computing in finite extension of finite rings. User's manual.
Many computational problems need arithmetic operations in
polynomial finite rings of Z/nZ where n is an integer
(n>1). Integer factorizations, primality testing are for
instance such applications. To solve them, programmers use
general symbolic mathematical softwares or write specific
programs (most of the time in C).
On the first hand,
symbolic mathematical softwares (Maple, Mathematica,...)
handle with difficulty computations in finite fields. In the
worst cases, such programs perform computations with
rationals before finally reducing the objects modulo the
characteristic n, in the best cases, such reductions are
performs but extensions of a finite ring cannot be
implemented. In any cases, applications written with such
softwares are ten to hundred times slower than an “ad hoc”
implementation in C. On the other hand, optimized C
libraries deal only with one side of finite fields, mainly
We hardly believe we can keep the efficiency of
these C libraries while working in any polynomial extension
of Z/nZ. We designed the ZEN library to perform
efficient arithmetic operations in these sets.
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